FIG. 1 illustrates the sea surface height and a satellite measuring the sea surface height with an altimeter. Sea surface height is the deviation in sea surface level from the marine geoid, an expected value that takes into account the earth's gravity and the bottom topography of the ocean. Sea surface height can also be affected by ocean eddies, temperature of the upper ocean water, tides in the deep ocean, and ocean currents or ocean circulation.
NASA began tracking ocean surface topography in 1992 with TOPEX/Poseidon, a joint US-French space mission from an orbit 1336 km above the ocean surface. In addition, the JASON-1 spacecraft was launched in 2001 to track ocean surface topography. The spacecrafts' radar altimeters measure the precise distance between the satellite and sea surface by measuring the round-trip travel time of microwave pulses bounced from the spacecraft to the sea surface and back to the spacecraft. The satellite's position is known from laser measurements and by triangulation with GPS satellites. The altitude of the satellite is determined by a sophisticated estimation procedure based on an orbit determination measurement system both onboard the satellite and on the ground stations located all over the world. The details of the shape of the returned radar pulses also provide information on wave height.
Since the TOPEX/POSEIDON satellite was launched, models have been developed and applied to the altimetry measurements, with a goal improving the accuracy of the sea surface height measurements.
During an eight month period after launch, Jason-1 was in a verification phase in which its orbit was positioned to sample the ocean within 1 km of the nominal ground track at the equator and 72 seconds ahead of the T/P satellite, as discussed in Menard, Y., L.-L. Fu, P. Escudier, F. Parisot, J. Perbos, P. Vincent, S. Desai, B. Haones, and G. Kunstmann, “The Jason-1 mission”, Marine Geodesy, Vol. 26, pages 131-146 (2003). After the verification tandem phase, T/P was repositioned into a ground track interleaved with the Jason-1 orbit to begin a scientific tandem phase.
One important application of satellite altimeter data is the estimation of the zonal and meridional components of the geostrophic velocity fields. Prior to the beginning of the scientific tandem phase, a crossover method was the primary way to estimate geostrophic velocities from exact repeat orbit satellite measurements at the intersections of ascending and descending tracks. A crossover method is discussed in Parke, M. E., R. L. Stewart, D. L. Farless, and D. E. Cartwright, “On the choice of orbits for an altimetric satellite to study ocean circulation and tides”, J. Geophysical. Research. Vol 92, issue/pages: 11,693-11,707 (1987).
During the scientific tandem phase, Jason-1 and T/P have coordinated orbits with half the spacing (ground-track separation) of the original T/P mission. At the equator, the T/P spacing is approximately 79 km. Stammer, D., and C. Dietrich, “Space-borne measurements of the time-dependent geostrophic ocean flow field”, J. Atmos. Oceanic Technol., Vol. 16, pages 1198-1207 (1999) discuss a parallel track method for estimating the zonal and meridional components of the geostrophic velocity fields from between-track differences of sea surface height measured with the altimeters on Jason-1 and T/P during the scientific tandem phase.
Sea state bias (SSB) is a correction that is applied to the calculated sea surface height (based on the satellite altimeter) to account for differences in the reflection of the radar pulse due to surface waves. Vincent, P., Desai, S. D., Dorandeu, J., Ablain, M., Soussi, B., Callahan, P. S., and B. J. Haines, “Jason-1 Geophysical Performance Evaluation”, Marine Geodesy, Vol. 26, pages167-186 (2003) discusses the sea state bias correction and indicates that the differences in the reflection of the radar pulse due to surface waves cause the largest part of the error in the range measurements of Jason-1 and T/P.
The sea state bias has been estimated empirically by fitting data to a relationship between sea state bias, surface wave height, and wind speed, as discussed in Gaspar, P., Ogor, F., Le Traon P. Y., and O. Z. Zanife, “Estimating the sea state bias of the TOPEX and POSEIDON altimeters from crossover differences”, J. Geophys. Res., Vol. 99, pages 24,981-24,994 (1994) and in Chambers, D. P., S. A. Hayes, J. C. Ries, and T. J. Urban, “New TOPEX sea state bias models and their effect on global mean sea level”, J. Geophys. Res. 108(C10), 3305, doi:10.1029/2003JC001839 (2003). Nonparametric methods are discussed in Gaspar, P., and J. P. Florens, “Estimation of the sea state bias in radar altimeter measurements of sea level: Results form a new nonparametric method”, J. Geophys. Res., Vol.103, pages 15,803-15,814 (1998) and in Gaspar, Labroue, S., Ogor, F., Lafitte, L., Marchal, L., and M. Rafanel, “Improving nonparametric estimates of the sea state bias in radar altimeter measurements of sea level”, J. Atmos. Oceanic Technol., Vol. 19, pages 1690-1707 (2001). These models assume the sea state bias is a global estimate with no spatial or directional dependence.